Algorithm Overview

Atmosphere Profile Algorithm

In order for atmospheric temperature to be inferred from measurements of thermal emission, the source of emission must be a relatively abundant gas of known and uniform distribution. Otherwise, the uncertainty in the abundance of the gas will make ambiguous the determination of temperature from the measurements. There are two gases in the earth-atmosphere that are present in uniform abundance for altitudes below about 100 km, and show emission bands in the spectral regions that are convenient for measurement. Carbon dioxide, a minor constituent with a relative volume abundance of 0.003, has infrared vibrational-rotational bands. Oxygen, a major constituent with a relative volume abundance of 0.21, also satisfies the requirement of a uniform mixing ratio and has a microwave spin-rotational band. In addition, the emissivity of the earth surface in the surface sensitive spectral bands must be characterized and accounted for.

There is no unique solution for the detailed vertical profile of temperature or an absorbing constituent because (a) the outgoing radiances arise from relatively deep layers of the atmosphere, (b) the radiances observed within various spectral channels come from overlapping layers of the atmosphere and are not vertically independent of each other, and (c) measurements of outgoing radiance possess errors. As a consequence, there are a large number of analytical approaches to the profile retrieval problem. The approaches differ both in the procedure for solving the set of spectrally independent radiative transfer equations (e.g., matrix inversion, numerical iteration) and in the type of ancillary data used to constrain the solution to insure a meteorologically meaningful result (e.g., the use of atmospheric covariance statistics as opposed to the use of an a priori estimate of the profile structure). There are some excellent papers in the literature which review the retrieval theory which has been developed over the past few decades (Fleming and Smith, 1971; Fritz et al., 1972; Rodgers, 1976; Twomey, 1977; and Houghton et al. 1984). The following sections present the mathematical basis for two of the procedures which have been utilized in the operational retrieval of atmospheric profiles from satellite measurements.

Statistical Regression Profile Retrieval

A computationally efficient method for determining temperature and moisture profiles from satellite sounding measurements uses previously determined statistical relationships between observed (or modeled) radiances and the corresponding atmospheric profiles. This method is often used to generate a first-guess for a physical retrieval algorithm, as is done in the International TOVS Processing Package (ITPP, Smith et al., 1993). The statistical regression algorithm for atmospheric temperature is described in detail in Smith et. al. (1970), and can be summarized as follows (the algorithm for moisture profiles is formulated similarly). In cloud-free skies, the radiation received at the top of the atmosphere at frequency ν is the sum of the radiance contributions from the Earth’s surface and from all levels in the atmosphere,